Method and system of profiling display power

ABSTRACT

A method of determining a model for pixel power consumption for each pixel in a display of a device displaying each color in a color space is disclosed which includes establishing a color space for the display, decomposing the color space into a plurality of subgrids, measuring the pixel power associated with a selected set of colors in each subgrid of the plurality of subgrids, establishing a pixel power model for each subgrid of the plurality of subgrids by applying a function to the power values at the selected set of colors in that subgrid, and deriving a piecewise pixel power model for the entire color space which includes pixel power models for the plurality of subgrids.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present non-provisional patent application is related to and claimsthe priority benefit of U.S. Provisional Patent Application Ser. No.63/212,717, entitled A METHOD OF PROFILING DISPLAY POWER which was filedJun. 20, 2021, the contents of which are hereby incorporated byreference in its entirety into the present disclosure.

STATEMENT REGARDING GOVERNMENT FUNDING

None.

TECHNICAL FIELD

The present disclosure generally relates to power profiling ofelectronics, and in particular, to a method for profiling the powerusage of displays.

BACKGROUND

This section introduces aspets that may help facilitate a betterunderstanding of the disclosure. Accordingly, these statements are to beread in this light and are not to be understood as admissions about whatis or is not prior art.

Optimizing the battery drain of mobile apps helps to extend the mobiledevice battery life which is critical to the mobile experience of the 5+billion phone users (over half are smartphones). Optimizing the batterydrain of mobile apps requires optimizing the battery drain of all majorpower-consuming components, including CPU, GPU, display, WiFi/LTE, GPS,and hardware decoder. After over a decade of phone evolution, displayhas remained as one of the major power-draining components in modernsmartphones.

The latest display technology, Organic light-emitting diode (OLED), useslight-emitting diode as pixels and therefore omits the need for externalbacklight used in its predecessor liquid crystal display (LCD), and indoing so provides much better power efficiency than LCD. Due to itspower efficiency and several other advantages (thinner, lighter, andmore flexible) over LCD and standard LED, OLED has seen wide adoption inhigh-end and mid-range smartphones.

OLED power draw is directly related to the displayed content. Thus anyreal potential of OLED power savings lies in exploiting the appUserInterface (UI) color design, i.e., how to design the app UI to usepixel colors that result in less OLED display power draw. These includemanual designs by app developers as well as automatic colortransformations.

One of the extreme examples of color transformation to save displayenergy of mobile devices is the recent wide adoption of dark-themedcolor contents, known as dark mode, by both Android and iOS which addeddark mode as one of major features in their recent OS update, and appvendors who quickly rolled out dark mode UI options in their latest appreleases.

Despite the industry's major push for dark mode, it remains unclear howmuch power and energy savings dark mode will bring to the apps, as theOLED display power saving from switching from the normal (or light) todark mode depends on the displayed content, which can vary significantlyfrom one app to another, and from one app activity to the next. Moregenerally, the industry is lacking an OLED display power profiling toolthat can accurately estimate the OLED display power draw and attributeit to the individual UI components. Such a tool will enable an appdeveloper to gain instant insight into how different UI designs affectthe OLED display power draw in running the app on specific mobiledevices and optimize the app UI design accordingly.

Therefore, there is an unmet need for a novel approach to accuratelyprofile the power usage of displays, in particular of OLED displays.

SUMMARY

A method of determining a model for pixel power consumption for eachpixel in a display of a device displaying each color in a color space isdisclosed. The method includes establishing a color space for thedisplay, decomposing the color space into a plurality of subgrids,measuring the pixel power associated with a selected set of colors ineach subgrid of the plurality of subgrids, establishing a pixel powermodel for each subgrid of the plurality of subgrids by applying afunction to the power values at the selected set of colors in thatsubgrid, and deriving a piecewise pixel power model for the entire colorspace which includes pixel power models for the plurality of subgrids.

A method of determining power consumption by a display of a device isalso disclosed. The method includes receiving a piecewise pixel powermodel for a color space for the display, wherein the piecewise pixelpower model is based on the pixel power models for a plurality ofsubgrids constituting the color space supported by the display,recording a frame comprising a plurality of pixels, determining to whichsubgrid of the plurality of subgrids each pixel of the plurality ofpixels belong, applying the piecewise pixel power model to each pixel toestimate the power draw associated with the associated pixel, summing upall the estimated powers for the plurality of pixels, and adding aconstant baseline power draw value associated with running the displayto the estimated power for all the pixels to thereby generate an overallpower draw associated with the display, wherein the constant baselinepower is a difference between total power draw of the device displayinga static image where all pixels are set to zero, and total power of thedevice when the display is deactivated.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 provides graph 3-dimensional graphs of current draw for differentmodels (a: PIXEL 2, b: MOTO Z3, c: PIXEL 4, and d: PIXEL 5) varying redand blue in the color space while maintaining green constant at 112.

FIG. 2 is a flowchart that describes the operations of the modelingapproach of the present disclosure.

FIG. 3 is a flowchart depicting method steps for measuring per-pixelpower for each subgrid point, according to the present disclosure.

FIG. 4 is a flowchart depicting how to apply the model according to oneembodiment of the present disclosure wherein the model is applied toeach pixel without any sampling (sampling is defined as a regularspacing between pixels which requires multiplication of power by thesampling size in order to determine the overall power).

FIG. 5 is a flowchart depicting a method for adaptively partitioning thecolor space, according to the present disclosure.

FIG. 6 is an example of a computer system that can interface with anexternal power monitoring device and a device with a display whose powerconsumption is of interest.

DETAILED DESCRIPTION

For the purposes of promoting an understanding of the principles of thepresent disclosure, reference will now be made to the embodimentsillustrated in the drawings, and specific language will be used todescribe the same. It will nevertheless be understood that no limitationof the scope of this disclosure is thereby intended.

In the present disclosure, the term “about” can allow for a degree ofvariability in a value or range, for example, within 10%, within 5%, orwithin 1% of a stated value or of a stated limit of a range.

In the present disclosure, the term “substantially” can allow for adegree of variability in a value or range, for example, within 90%,within 95%, or within 99% of a stated value or of a stated limit of arange.

A novel approach is presented herein to accurately model the power usageof displays, in particular of OLED displays, in displaying any contentTowards this end, an accurate per-frame OLED display power profiler,PFOP, is presented that helps developers to gain insight into the impactof different app UI designs on its OLED power draw.

Power modeling of OLED display has been studied over the past decade,first on external display then earlier smartphones. It is thus useful todetermine whether the prior-art power models of OLED display proposed inthe past decade can accurately capture the power behavior of OLEDdisplays on modern smartphones. To answer this question, a measurementstudy was carried out to characterize the power behavior of OLEDdisplays on four representative smartphones from four recentgenerations, PIXEL 2 (2017), MOTO Z3 (2018), PIXEL 4 (2019) AND PIXEL 5(2020). The study revealed unique power draw behavior of modern phoneOLED displays: (1) The OLED display power draw violates thesuperposition property previously reported based on pixel power simplesummation displaying the three base colors: red, green and blue afterremoving base power—e.g., the power draw in displaying the white colorcan be far less than the simple summation; and (2) The OLED displaypower often violates the monotonicity principle, that the power draw indisplaying canonically larger RGB values in the color space should behigher. The two findings suggest that previously proposed linear andnon-linear OLED power models are unlikely to achieve high predictionaccuracy, as confirmed by the study.

Since an OLED display includes N pixels that emit lights independentlyof each other, the total power draw of an OLED display equals the sum ofthe power draw P_(i) by individual pixels:

$\begin{matrix}{P_{OLED} = {C + {\sum\limits_{i = 1}^{N}P_{i}}}} & (1)\end{matrix}$where C is a baseline power usage which is a constant and accounts forthe power draw by the nonpixel component of the OLED display, alsodenoted as dark screen power, and P_(i) represents individual pixelpower draw which depends on the pixel color value.

To facilitate measurements of OLED display power for different coloredpixels, a simple Android app was created that displays a static image ata time on the screen, while the phone power draw is being measured. Theimages used will have the same dimension as the screen, e.g., 1920×1080pixels on GOOGLE Pixel 2. In one implementation, for each of the staticcolored images, we generated 5 measurements, out of which we chose 3that had the least standard deviation and took the average. First, wemeasured the CPU idle power as the power draw when the screen is off andthe app is running using a wakelock (a mechanism that ensures the deviceremains on). Second, we measure the OLED dark screen power by displayinga dark screen with all the pixel values set to zero and then subtractthe CPU idle power (from Step 1) from the measured phone power in orderto determine the constant C of equation (1). Finally, to measure thepower draw by all the colored pixels, i.e., in

$\sum\limits_{i = 1}^{N}P_{i}$in displaying a static image, we measure the phone power and subtractfrom it both the dark screen power and the CPU idle power. The aboveprocess is accurate as in all three steps, the CPU utilization remainssteady at 2.5%, 4.9%, 1.7% and 2.6% on PIXEL 2, MOTO Z3, PIXEL 4, ANDPIXEL 5, respectively.

To understand the power usage, the first question to be answered iswhether the power draw of the three subpixels are independent, i.e.,whether they satisfy the superposition property which states that thepower consumed by three subpixels are additive, as discussed below withregards to Equation (2).

Directly measuring the power draw of every pixel color is too costly(e.g., it would take 256³×2 seconds or 1.06 years following ourmethodology of displaying each image for 2 seconds for a brute forceapproach of sweeping the 3-D RGB color space, with each base colorintensity varied from 0 to 255 (in the sRGB space)), power profilingmust be carried out based on a modeling. Different approaches have beenproposed in the prior art. According to one approach, pixel power drawis modeled as the simple summation of the power draw of each of thesubpixels:P _(i)(R _(i) ,G _(i) ,B _(i))=f(R _(i))+g(G _(i))+h(B _(i))  (2)

However, because of interdependencies of driving circuits, this simplesummation of subpixels proves to be inaccurate for OLED displays. Inorder to remedy this inaccuracy, others have applied a weighing approachto (2) utilizing, e.g., a linear regression, in order to minimize theerror. However, this method still suffers from interdependencies. Toaccount for interdependencies, others in the prior art added non-linearterms to the model before applying linear regression techniques.However, all these suffer from a fundamentally flawed assumption ofapplying a linear solution to a non-linear problem. Referring to FIG. 1, the current draw for different models (a: PIXEL 2, b: MOTO Z3, c:PIXEL 4, and d: PIXEL 5) is shown with varying red and blue in the colorspace while maintaining green constant at 112. In each case, it can beseen that the surface defined in the associated 3D graph, i.e. the powerdraw in varying the red and blue intensities, is not linear across therange of red and blue intensity values, while the approach in the priorart assumes such linearity.

To account for this non-linearity the inventors of the presentdisclosure have developed a novel approach to divide the aforementionedsurface into subdivisions that are either (1) equally sized, or (2)adaptively sized based on the linearity criterion. By treating eachappropriately sized subdivision, a linear solution, e.g., a linearregression, can be applied in order to accurately model power usage.

Referring to FIG. 2 , a flowchart is presented that describes theoperations of the modeling approach of the present disclosure. Themethod 200 shown in FIG. 2 , begins by decomposing the color space intosubgrids, as shown in step 202. As discussed above, these subdivisionscan be equal in size or adaptively chosen as described further below.Next, the method measures each pixel power value corresponds to thecolor at each grid point, as provided in step 204. This process isdescribed further in reference with FIG. 3 , below. Next the methodincludes deriving the Pixel power model for each of the subgrids byapplying linear regression to the linear terms or both linear andnon-linear terms of power values at its eight corners (an example ofwhich is shown in FIG. 2 ), as provided in step 206. Next, the Pixelpower model for all the subgrids constitute the piecewise Pixel powermodel for the complete color space, as provided in steps 208.

Referring to FIG. 3 , a method 300 with steps for measuring per-pixelpower for each subgrid point is presented. The method 300 of FIG. 3begins by connecting a device for which display power profiling isdesired to an external power monitoring device (see FIG. 6 ) in order tomeasure the total device power draw, as provided in step 302. Next themethod includes deactivating the display, as provided in step 304. Next,the method includes determining the total device power draw with displayturned off but the device otherwise running, as provided in step 306.This power draw is denoted as X. Next, the display is turned on with astatic dark image (all pixel values are set to zero) and the totaldevice power is measured, as provided in step 308. This power is denotedas Y. Next the method subtracts X from Y to determine the constant powerdraw of the display denoted as C in equation (1), as provided in step310. Next the method displays a static image with all pixels set to thetarget value corresponding to a point of the subgrid discussed withreference to FIG. 2 , and the total power is again measured, as providedin step 312. This power is denoted as Z. Next the method subtracts Yfrom Z and divides by the total number of pixels to determine theper-pixel power draw for the subgrid point: ((Z−Y)/Number_of_pixels), asprovided in step 314.

With the piecewise pixel power model for the display developed, themodel can be applied to determine the total power usage of the displayin displaying a frame of any given pixel content. Referring to FIG. 4 ,a flowchart is presented for a method 400 on how to apply the modelaccording to one embodiment. In this embodiment, the model is applied toeach pixel without any sampling (sampling is defined as a regularspacing between pixels which requires multiplication of power by thesampling size in order to determine the overall power). While not shown,the sampling approach is another embodiment according to the presentdisclosure for determining overall power usage.

Referring to FIG. 4 , the model is applied by first recording a frame,as provided in step 402. Next the method determines the sRGB subgrid ofthe color space to which each pixel (or each sampled pixel according tothe sampling embodiment) belongs, as provided in step 404. Next, themethod applies the pixel power model of the corresponding subgrid toestimate the power drawn for that pixel, as provided in step 406. Next,the model sums up all the estimated power for all the pixels to obtainthe frame OLED display power, as provided in step 408. Finally theconstant C from equation (1) found in the steps of FIG. 3 is added todetermine the overall power usage of the display, as provided in step410.

As described above, in deriving the piecewise power model for thedisplay, the partitioning of the color space can be based onequally-sized subdivisions, or based on an adaptive subgridpartitioning. The adaptive subgrid partitioning aims to find the largestsubdivision for which the linear solution, e.g., the linear regression,is appropriate. Towards this end and with reference to FIG. 5 , a method500 for adaptively partitioning the color space is provided. The method500 begins by measuring the pixel power value corresponding to the colorof each grid point of the input subgrid of the color space, as providedin step 502. Next the method includes deriving the pixel power model(liner model or non-linear model) for the input subgrid by applyinglinear regression to the power values at its eight corners (see FIG. 2), as provided in step 504. Next the method includes estimating theaccuracy of the derived power model by comparing the estimated power ofa set of colors within the subgrid with the actual power measurement indisplaying each of those colors, as provided in step 506. If the averageerror is higher than a threshold, partition the input subgrid into equalsized subgrids, and recursively invoke the current process on each newsubgrid, as provided in step 508. In this approach, the recursivepartitioning of the subgrid can be based on a power of 2, e.g., into 8new subgrids, or a power of 3, e.g., into 27 new subgrids, and so on.

Referring to FIG. 6 , an example of a computer system is provided thatcan interface with the above-discussed external power monitoring device.And the device whose display power consumption is of interest. Referringto FIG. 6 , a high-level diagram showing the components of an exemplarydata-processing system 1000 for analyzing data and performing otheranalyses described herein, and related components. The system includes aprocessor 1086, a peripheral system 1020, a user interface system 1030,and a data storage system 1040. The peripheral system 1020, the userinterface system 1030 and the data storage system 1040 arecommunicatively connected to the processor 1086. Processor 1086 can becommunicatively connected to network 1050 (shown in phantom), e.g., theInternet or a leased line, as discussed below. The imaging described inthe present disclosure may be obtained using imaging sensors 1021 and/ordisplayed using display units (included in user interface system 1030)which can each include one or more of systems 1086, 1020, 1030, 1040,and can each connect to one or more network(s) 1050. Processor 1086, andother processing devices described herein, can each include one or moremicroprocessors, microcontrollers, field-programmable gate arrays(FPGAs), application-specific integrated circuits (ASICs), programmablelogic devices (PLDs), programmable logic arrays (PLAs), programmablearray logic devices (PALs), or digital signal processors (DSPs).

Processor 1086 can implement processes of various aspects describedherein. Processor 1086 can be or include one or more device(s) forautomatically operating on data, e.g., a central processing unit (CPU),microcontroller (MCU), desktop computer, laptop computer, mainframecomputer, personal digital assistant, digital camera, cellular phone,smartphone, or any other device for processing data, managing data, orhandling data, whether implemented with electrical, magnetic, optical,biological components, or otherwise. Processor 1086 can includeHarvard-architecture components, modified-Harvard-architecturecomponents, or Von-Neumann-architecture components.

The phrase “communicatively connected” includes any type of connection,wired or wireless, for communicating data between devices or processors.These devices or processors can be located in physical proximity or not.For example, subsystems such as peripheral system 1020, user interfacesystem 1030, and data storage system 1040 are shown separately from thedata processing system 1086 but can be stored completely or partiallywithin the data processing system 1086.

The peripheral system 1020 can include one or more devices configured toprovide digital content records to the processor 1086. For example, theperipheral system 1020 can include digital still cameras, digital videocameras, cellular phones, or other data processors. The processor 1086,upon receipt of digital content records from a device in the peripheralsystem 1020, can store such digital content records in the data storagesystem 1040.

The user interface system 1030 can include a mouse, a keyboard, anothercomputer (connected, e.g., via a network or a null-modem cable), or anydevice or combination of devices from which data is input to theprocessor 1086. The user interface system 1030 also can include adisplay device, a processor-accessible memory, or any device orcombination of devices to which data is output by the processor 1086.The user interface system 1030 and the data storage system 1040 canshare a processor-accessible memory.

In various aspects, processor 1086 includes or is connected tocommunication interface 1015 that is coupled via network link 1016(shown in phantom) to network 1050. For example, communication interface1015 can include an integrated services digital network (ISDN) terminaladapter or a modem to communicate data via a telephone line; a networkinterface to communicate data via a local-area network (LAN), e.g., anEthernet LAN, or wide-area network (WAN); or a radio to communicate datavia a wireless link, e.g., WiFi or GSM. Communication interface 1015sends and receives electrical, electromagnetic or optical signals thatcarry digital or analog data streams representing various types ofinformation across network link 1016 to network 1050. Network link 1016can be connected to network 1050 via a switch, gateway, hub, router, orother networking device.

Processor 1086 can send messages and receive data, including programcode, through network 1050, network link 1016 and communicationinterface 1015. For example, a server can store requested code for anapplication program (e.g., a JAVA applet) on a tangible non-volatilecomputer-readable storage medium to which it is connected. The servercan retrieve the code from the medium and transmit it through network1050 to communication interface 1015. The received code can be executedby processor 1086 as it is received, or stored in data storage system1040 for later execution.

Data storage system 1040 can include or be communicatively connectedwith one or more processor-accessible memories configured to storeinformation. The memories can be, e.g., within a chassis or as parts ofa distributed system. The phrase “processor-accessible memory” isintended to include any data storage device to or from which processor1086 can transfer data (using appropriate components of peripheralsystem 1020), whether volatile or nonvolatile; removable or fixed;electronic, magnetic, optical, chemical, mechanical, or otherwise.Exemplary processor-accessible memories include but are not limited to:registers, floppy disks, hard disks, tapes, bar codes, Compact Discs,DVDs, read-only memories (ROM), erasable programmable read-only memories(EPROM, EEPROM, or Flash), and random-access memories (RAMs). One of theprocessor-accessible memories in the data storage system 1040 can be atangible non-transitory computer-readable storage medium, i.e., anon-transitory device or article of manufacture that participates instoring instructions that can be provided to processor 1086 forexecution.

In an example, data storage system 1040 includes code memory 1041, e.g.,a RAM, and disk 1043, e.g., a tangible computer-readable rotationalstorage device such as a hard drive. Computer program instructions areread into code memory 1041 from disk 1043.

Processor 1086 then executes one or more sequences of the computerprogram instructions loaded into code memory 1041, as a resultperforming process steps described herein. In this way, processor 1086carries out a computer implemented process. For example, steps ofmethods described herein, blocks of the flowchart illustrations or blockdiagrams herein, and combinations of those, can be implemented bycomputer program instructions. Code memory 1041 can also store data, orcan store only code.

Various aspects described herein may be embodied as systems or methods.Accordingly, various aspects herein may take the form of an entirelyhardware aspect, an entirely software aspect (including firmware,resident software, micro-code, etc.), or an aspect combining softwareand hardware aspects. These aspects can all generally be referred toherein as a “service,” “circuit,” “circuitry,” “module,” or “system.”

Furthermore, various aspects herein may be embodied as computer programproducts including computer readable program code stored on a tangiblenon-transitory computer readable medium. Such a medium can bemanufactured as is conventional for such articles, e.g., by pressing aCD-ROM. The program code includes computer program instructions that canbe loaded into processor 1086 (and possibly also other processors), tocause functions, acts, or operational steps of various aspects herein tobe performed by the processor 1086 (or other processors). Computerprogram code for carrying out operations for various aspects describedherein may be written in any combination of one or more programminglanguage(s), and can be loaded from disk 1043 into code memory 1041 forexecution. The program code may execute, e.g., entirely on processor1086, partly on processor 1086 and partly on a remote computer connectedto network 1050, or entirely on the remote computer.

The processor 1086 is coupled to the external power monitoring device1200 which is coupled to the device 1100 with the display 1102 whosepower consumption is of interest. As discussed above with respect toFIGS. 2-5 , the processor communicates with the device 1100 in order todrive the display 1102 and processes in the device 1100 while theexternal power monitoring device 1200 monitors power consumption of thedevice 1100, as discussed above. The methods discussed herein areperformed by software residing in non-transitory memory and which iscontrolled by the processor 1086.

Those having ordinary skill in the art will recognize that numerousmodifications can be made to the specific implementations describedabove. The implementations should not be limited to the particularlimitations described. Other implementations may be possible.

The invention claimed is:
 1. A method of determining a model for pixelpower consumption for each pixel in a display of a device displayingeach color in a color space, comprising: establishing a color space forthe display; decomposing the color space into a plurality of subgrids;measuring the pixel power associated with a selected set of colors ineach subgrid of the plurality of subgrids; establishing a pixel powermodel for each subgrid of the plurality of subgrids by applying afunction to the power values at the selected set of colors in thatsubgrid; and deriving a piecewise pixel power model for the entire colorspace which includes pixel power models for the plurality of subgrids.2. The method of claim 1, wherein the function is based on linerregression on linear terms of the power values.
 3. The method of claim1, wherein the function is based on liner regression on linear andnon-linear terms of the power values.
 4. The method of claim 1, whereineach subgrid of the plurality of subgrid is cubical, wherein the numberof corners of each cube is
 8. 5. The method of claim 1, wherein eachsubgrid of the plurality of subgrids is equally sized.
 6. The method ofclaim 1, wherein size of each subgrid of the plurality of subgrids isadaptively determined based on estimating the power of a set of colorswithin each subgrid of the plurality of subgrids and comparing thatestimate with the actual power measurement in displaying each color inthe set of colors.
 7. The method of claim 1, where the selected set ofcolors in each subgrid correspond to the eight corners of the subgrid.8. The method of claim 1, wherein the pixel power measurement associatedwith each color in the selected set of colors of each subgrid of theplurality of subgrids, includes: coupling the device to an externalpower monitoring device; disabling the display; measuring total powerdraw by the device with the display disabled (X); enabling the displayby providing a static image with all pixels of the image set to zero andmeasuring the total power draw by the device (Y); subtracting X from Y(Y−X) to obtain a constant baseline power draw associated with thedisplay (C); enabling the display by providing a static image with allpixels of the image set to each said color and measuring the total powerdraw by the device (Z); subtracting Y from Z to obtain the total powerdraw (Z−Y) by the pixels for said color; and dividing the total powerdraw Z-Y by the number of pixels.
 9. The method of claim 1, wherein thedisplay is an organic light emitting diode-based.
 10. The method ofclaim 1, wherein the device is a cellular phone.
 11. A method ofdetermining power consumption by a display of a device, comprising:receiving a piecewise pixel power model for a color space for thedisplay, wherein the piecewise pixel power model is based on the pixelpower models for a plurality of subgrids constituting the color spacesupported by the display; recording a frame comprising a plurality ofpixels; determining to which subgrid of the plurality of subgrids eachpixel of the plurality of pixels belong; applying the piecewise pixelpower model to each pixel to estimate the power draw associated with theassociated pixel; summing up all the estimated powers for the pluralityof pixels; and adding a constant baseline power draw value associatedwith running the display to the estimated power for all the pixels tothereby generate an overall power draw associated with the display,wherein the constant baseline power is a difference between total powerdraw of the device displaying a static image where all pixels are set tozero, and total power of the device when the display is deactivated. 12.The method of claim 11, wherein the display is an organic light emittingdiode-based.
 13. The method of claim 11, wherein the device is acellular phone.
 14. The method of claim 11, wherein spacing between eachpixel of the plurality of pixels is one.
 15. The method of claim 14,wherein the estimated power for the plurality of pixels is multiplied byK² before adding the constant baseline power draw associated withrunning the display.
 16. The method of claim 11, wherein spacing betweeneach pixel of the plurality of pixels is K.